Microsoft’s guidance when migrating Lync 2010 to Lync 2013 is to install the latest cumulative update for Lync 2010. This would also be my recommendation, however if you are wanting to know if your current Lync 2010 infrastructure can support a migration to Lync 2013, the minimum requirement is Lync 2010 CU7 (October 2012). This was the latest update at the time Lync 2013 RTM was released.
From my own experience it is not recommended to have Lync 2010 CU6 in coexistence with Lync 2013(CU3). In my scenario most of user and RGS where located on 2010 and few users where on 2013. I experienced unclear RGS problems and crashes (only few workflows) until 2010 was updated to CU10.
Cheers for letting me know your experience. As mentioned the latest update is always best, but maybe a a better minimum requirement would be CU7 since it was released around the same time as Lync 2013 RTM.
Lync 2013 Preview – Released July 2012
4.0.7577.199 June 2012 (CU6) http://support.microsoft.com/kb/2701585
Lync 2013 RTM – Released 11th October 2012
4.0.7577.203 October 2012 (CU7) http://support.microsoft.com/kb/2737915
I have updated my blog post to recommendation to CU7 as a minimum.